Non-Perturbative Collider Phenomenology of Stealth Dark Matter Ethan T. Neil (CU Boulder/RIKEN BNL) for the LSD Collaboration USQCD All Hands Meeting May 1, 2015
L attice S trong D ynamics Collaboration Xiao-Yong Jin Joe Kiskis James Osborn Rich Brower Oliver Witzel Michael Cheng Evan Berkowitz Claudio Rebbi Enrico Rinaldi Evan Weinberg Chris Schroeder Ethan Neil Pavlos Vranas Ethan Neil David Schaich Sergey Syritsyn Tom Appelquist Meifeng Lin George Fleming Mike Buchoff Graham Kribs 2
Strongly-coupled composite dark matter • Our focus: composite DM as a strongly-bound state of some more fundamental objects (think of the neutron) • Non-Abelian SU(N D ) gauge sector, with some fermions in the fundamental rep. Not the only possibility (e.g. “dark atoms”, other non-Abelian theories) but a well-motivated, somewhat familiar foundation. • Constituents can carry SM charges, and charged excited states active in early universe. Composite DM relic interacts via SM particles ( photon , Higgs ) but with form factor suppression!
Symmetries of stealth DM • Start with SU(N D ) gauge theory and N F Dirac fermions, in the fundamental rep, and impose some conditions. • First requirement: baryons are bosons - even N D . No magnetic moment. N D ≥ 4 gives automatic DM stability from Planck-scale violations. • Second requirement: couplings to electroweak and Higgs - one EW doublet and one singlet, N F ≥ 3. Ensures meson decay as well. • Third requirement: custodial SU(2) for electroweak precision - N F =4. As a bonus, charge radius is eliminated —> stealth DM!
Stealth dark matter: model details Field SU ( N D ) ( SU (2) L , Y ) Q • SU(4) gauge group with ! ! F u +1 / 2 1 F 1 = ( 2 , 0) 4 Dirac fermions (SU(2) L N F d − 1 / 2 1 ! ! and SU(2) R doublets) F u +1 / 2 2 F 2 = ( 2 , 0) N F d − 1 / 2 2 F u ( 1 , +1 / 2) +1 / 2 N 3 • Two sources of mass F d ( 1 , − 1 / 2) − 1 / 2 N 3 F u allowed: vector-like and ( 1 , +1 / 2) +1 / 2 N 4 F d ( 1 , − 1 / 2) − 1 / 2 N 4 Higgs-Yukawa EW-preserving mass: • Custodial symmetry is 1 F j L � M 12 ✏ ij F i 2 � M u 34 F u 3 F d 4 + M d 34 F d 3 F u 4 + h.c., identified as u <—> d EW-breaking mass: exchange symmetry L � y u 14 ✏ ij F i 1 H j F d 4 + y d 14 F 1 · H † F u 4 23 F 2 · H † F u � y d 23 ✏ ij F i 2 H j F d 3 � y u 3 + h.c. ,
Mass eigenstates • Two sources of mass, electroweak breaking and preserving. ∆ to be � � M ⌘ M 12 + M 34 M 12 � M 34 � � y 14 = y + ✏ y , y 23 = y � ✏ y , | ✏ y | ⌧ | y | . � , ∆ ⌘ � � 2 2 � ark fermion mass eigenvalues are • Assume yv<<M , to avoid vacuum alignment issues w/EWSB. Then two regimes arise, depending on the origin of the mass splitting: Linear Case: yv � ∆ Ψ d Ψ u 2 M u,d 2 2 y p ∆ 2 + y 14 y 23 v 2 / 2 M ± y Ψ = √ 2 M u,d 1 Ψ d Ψ u 1 1 Quadratic Case: yv ⌧ ∆ y Ψ = y 2 v 2 ∆ Q = − 1 Q = 1 2 (linear/quadratic effect observed before, see Hill and Solon 1401.3339) 2
Stealth dark matter on the lattice • The model: SU(4) gauge theory at [LSD collab., Phys. Rev. D89 (2014) 094508] moderately heavy Higgs exchange cross 0.8 Ê fermion mass spin-2 Ê 0.7 Ê Ê Ê Ê Ê spin-1 Ê Ê Ê 0.6 Ê spin-0 Ê Ê Ê Ê • On the lattice: 0.5 nucleons aM plaquette gauge 0.4 V action, Wilson Ê 0.3 Ê Ê Ê Ê Ê fermions (quenched) Ê 0.2 Π Ê Ê Ê 0.1 0.50 0.55 0.60 0.65 0.70 0.75 m PS ê m v • Spectrum shown to the right
Stealth dark matter: lattice results so far • Spectrum and scalar 훼 =0.64 5 ¥ 10 - 43 M PS ê M V = 0.70 DM - nucleon cross section H cm 2 L current calculation: mass 1 ¥ 10 - 43 훼 =0.16 5 ¥ 10 - 44 generation from Higgs 1 ¥ 10 - 44 훼 =0.04 5 ¥ 10 - 45 strongly constrained. 1 ¥ 10 - 45 훼 =0.01 5 ¥ 10 - 46 1 ¥ 10 - 46 LUX 10 50 100 500 1000 �� × �� - �� �� - ������� ����� ������� ���� �� ( �� � ) m B H GeV L �� × �� - �� • EM polarizability: lower �� × �� - �� �� × �� - �� bound on direct detection LEP �� × �� - �� for theories with charged cosmic ν �� × �� - �� constituents. Stealth DM �� × �� - �� visible below a TeV or so. �� �� ��� ��� ���� ���� m B (GeV) M B (GeV) � �� ( ��� )
. 'Es¥dsFniF .at#tiFiomDm4 ; La 4 . . - i¥#± i÷#i z Comparison between typical SUSY DM and composite DM: ^ E Li lightest baryon " " p SY composite • DM is far from lightest particle in the new sector! Much harder to produce directly in colliders, so MET signals are greatly suppressed. • On the other hand, presence of the much lighter and charged Π states gives strong bounds from complementary searches.
wo: Meson decay • Important consequence of electroweak coupling: allow mesons to decay, especially the charged ones! 0¥ ⇒ ¥ne¥I axial | Π ± i = if Π p µ h 0 | j µ • Mass flip in final state, due to decay of pseudoscalar bound state (same for QCD pions.) Gives preferred decay to heaviest SM states: ! m 2 0 ) = G 2 Γ ( Π + ! ff f 4 ⇡ f 2 F Π m 2 f m Π c 2 1 � axial m 2 Π
Meson production Π + f • First signature expected: γ Drell-Yan photon production of charged Π ¯ f Π − • To calculate rate, pion form factor needed at threshold: F V (Q 2 =4m Π 2 ) Breit-Wigner IAM with NLO l 6 10 • Hard to access at this 2 momentum on lattice. In | F π | QCD, “vector meson 1 dominance” does pretty well… (arXiv:0812.3270) 0.1 1 -500 0 500 1000 2 ) 1/2 (MeV) (q 2 ) 1/2 (MeV) -(-q
How the picture changes for m ρ below threshold: π - π scattering amplitude with m π =140 MeV, for QCD (m π /m ρ ~0.18) and for a stealth-DM-like theory (m π /m ρ ~0.55) (*note: this is not �� � F V (Q 2 ), it’s a Breit- Wigner model of I=1 π - π scattering.) ���� ��� m ρ = 770 MeV � �� ( � ) �� m ρ = 255 MeV � ���� s = 4 m 2 ���� π - ��� - ��� ��� ��� ��� ��� ��� ��� � ( ��� � ) • Here, “rho” resonance is below 2 π threshold - but it’s also much closer to the threshold. Vector-meson dominance should be reliable, but further study is needed • The “dark rho” is very narrow, since decay to ππ is closed. Another (TeV-scale) state to look for in colliders!
Our plan • Determine “stealth ρ ” decay a- ¥ Ent constant and calculate decay width ao •€ E÷ 2 ) at • Measure “stealth π ” F V (Q space-like momenta from three- point function (pion charge radius) • Combine with vector-meson dominance model to predict . 2 ) for collider production F V (4m Π . pion charge radius ρ width, mass ! Z ∞ h r 2 Π i Q 2 + Q 4 � 11 ( s ) F V ( Q 2 ) = exp ds s 2 ( s � Q 2 � i ✏ ) 6 ⇡ 4 m 2 Π (arXiv:0812.3270)
Electroweak precision • No T parameter by construction (custodial symm), but S parameter is an important constraint! Two asymptotic forms of S contribution: M 2 � M 1 y 2 v 2 1.0 Π 3 Y ( q 2 ) = 1 all (90% CL) y 2 v 2 + 2 ∆ 2 Π V V ( q 2 ) , Γ Z , σ had , R l , R q 8 asymmetries M W , Γ W M 1 ≈ M 2 0.5 e & ν scattering Π 3 Y ( q 2 ) ⇡ ✏ 2 y v 2 APV 4 M 2 Π LR ( q 2 ) = 0 T • Calculation of strong- coupling part yields -0.5 direct bounds on Yukawa couplings (important for -1.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 asymmetric relic density) (PDG 2014) S
Lattice calculation details • Form factor: calculate < π (t)V μ (t’) π (0)> and < π (t) π (0)>. Construct appropriate ratio to extract vector-current matrix element. • Three vector-current insertion locations, four sources per config —> 12 Wilson propagators; 500 (pure-gauge) configurations. • S-parameter: calculate conserved-local correlators <V C (x)V L (0)> and <A C (x)A L (0)>. Two source positions, L s =8. • By-products of DWF calculation: F π , mass renormalization (m f /M B ).
Resource request vol m PS L m PS /m V Cost (DWF) Cost (Wilson) Total cost β κ 32 3 × 64 11.028 0.1554 11.1 0.76 0.61 0.46 1.07 0.15625 9.2 0.69 — 0.68 1.58 0.1568 7.7 0.62 1.28 0.97 2.25 0.1572 6.6 0.55 — 1.36 3.16 0.1575 5.9 0.49 2.55 1.93 4.48 32 3 × 64 11.5 0.1523 6.1 0.69 0.90 0.68 1.58 Total 5.34 6.08 11.42 • Three mass points for domain-wall S parameter calculation; we expect mild mass dependence, based on experience • One point at β =11.5, to test discretization effects (spectroscopy here shows no significant deviations) • We are working on a new fully threaded/vectorized code base, meant to replace QDP/C; Wilson solver in progress. Up to 2x speed-up in calculations expected, but no benchmarks available yet, and we don’t include this factor above
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